Multi-phase resonant converter and method of controlling it

ABSTRACT

A PWM controlled multi-phase resonant voltage converter may include a plurality of primary windings powered through respective half-bridges, and as many secondary windings connected to an output terminal of the converter and magnetically coupled to the respective primary windings. The primary or secondary windings may be connected such that a real or virtual neutral point is floating.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/211,619, filed Dec. 6, 2018, which application is a continuation ofU.S. patent application Ser. No. 15/693,166, filed Aug. 31, 2017, nowU.S. Pat. No. 10,193,461, which is a divisional of U.S. patentapplication Ser. No. 12/820,549, filed on Jun. 22, 2010, now U.S. Pat.No. 9,780,678, which claims priority to Italian Application No.VA2009A000038, filed on Jun. 24, 2009, all applications are herebyincorporated herein by reference.

TECHNICAL FIELD

This invention relates to voltage converters and more particularly toswitching resonant voltage converters.

BACKGROUND

FIG. 1 is a high level block diagram of a switching resonant voltageconverter. Among resonant voltage converters having the basicarchitecture of FIG. 1, and that are classified based upon theconfiguration of the resonant circuit that is used, there is the LICresonant voltage converter. A half-bridge driven architecture of such aconverter is illustrated in FIG. 2.

For simplicity, reference will be made to half-bridge driven voltageconverters, though the addressed technical problems also affectfull-bridge driven voltage converters. One of the weak points of thisarchitecture, especially when functioning at high power levels (>1 kW),is tied to the AC current that flows through the output capacitorC_(OUT). This AC current has large peak and rms values that may requirethe use of a larger, and thus more encumbering bank of capacitors forthe capacitance C_(OUT) than for a forward voltage converter of the sameoutput voltage and power. This considerably burdens the LIC resonantconverter, especially in power applications of relatively large powerdensity such as, for example, power supply systems for servers or fortelecommunication systems, in which its high efficiency characteristicis particularly advantageous.

The multi-phase or “interleaving” techniques may prevent this drawback.A multi-phase voltage converter may be obtained by connecting inparallel two or more switching converters of a same architecture to makethem share the same input voltage generator, and supply the same outputload. Moreover, with an appropriate phase control of the driving signalsof the power switches, it may be possible to minimize or, in certaincases, even to practically nullify the ripple on the output current(sometimes even on the input current) of the converters.

Other advantages of the multi-phase approach are the possibility ofsubdividing the overall power requirement among a number of smallerconverters thus making a larger power density possible and optimizingefficiency over a larger interval of load currents using the “phaseshedding” technique. That is, turning off one or more phases when theload decreases, and managing the reduced requirement with a reducednumber of converters, thus reducing losses due to parasitic componentsof the power circuits that may become dominant with low powerconditions.

The interleaving technique achieves:

-   -   1) reduction of the ripple of the output and input currents of        the converter;    -   2) reduction of the power managed by each converter with a        consequent optimization of their dimensioning;    -   3) increased efficiency over a wide range of output load because        of the turning off one or more phase circuits when functioning        at low power and reduction of losses due to parasitic        components; and    -   4) greater power density and smaller form factor. To achieve the        above beneficial effects, it may be essential to ensure that the        load of the converter be subdivided as equally as possible among        the phase circuits. This is a serious obstacle to implementation        of “interleaving” techniques in multi-phase resonant voltage        converters.

To better illustrate the problem, reference is made to the three-phaseLIC resonant voltage converter of FIG. 4, though the same considerationshold for resonant converters of a different type and with any number ofphases. The distinct phase circuits are driven at the same frequency,and the driving signals of the power switches are mutually phased apartby 120° making the currents of the output diodes superpose withcontinuity. This functioning condition is illustrated in the time graphsof FIG. 5.

In a first harmonic approximation, the functioning of a single LLCresonant phase is quantitatively described by means of characteristiccurves, as the ones depicted in FIG. 6. In these figures the abscissa isthe operating frequency x, normalized to the series resonant frequencyassociated with the elements Cr and Ls of the resonant circuit of FIG.2, and the ordinate is the ratio M between the voltage on the nodes ofthe secondary winding, which is equal to the sum of the output voltageand the voltage drop on the secondary rectifiers translated to theprimary circuit, and the input voltage. Each characteristic curve isassociated to the quality factor Q of the resonant circuit that isinversely proportional to the output resistance R_(OUT). As aconsequence, Q is substantially proportional to the output currentI_(OUT), and each curve is substantially associated with a value of theload current.

The three phase circuits are powered with the same input voltage, they“see” the same output voltage, and work at the same frequency. If thethree phase circuits are exactly identical among them, they will workwith the same current amplitude, as shown in FIG. 5.

Nevertheless, in a real world implementation, the inevitable tolerancesof the components must be taken into consideration. Thus, the threephase circuits may have different values of the ratio M because of theeffect of different voltage drops on the respective secondary rectifiersand of different values of x, and/or of the proportionality constantbetween Q and I_(OUT) because of differences among the values of Ls, Crand Lp of the three resonant circuits. As a consequence, the currents inthe various phase circuits will differ, and one of them may even providethe whole power for the load, while the other phases may be inactive.

These theoretical predictions are confirmed by simulation. In thediagrams of FIG. 7 the same signals of FIG. 5 relating to the converterof FIG. 4 are shown, but the value of the capacitor Cr of the phasecircuit 2 is reduced by 10% and that of phase circuit 3 is increased by10%. The currents through phase circuits 1 and 3 are close to zero, andthe current of phase circuit 2 is almost equal to the output current.Solely phase circuit 2 is effectively working, and there is nointerleaving among the phase circuits. More precisely, compared with theideal case of FIG. 5, the average output current of phase circuit 1 isreduced by 97.4%, that of phase circuit 2 is increased by 297%, and thatof phase circuit 3 is zero; the peak-to-peak amplitude of the ripple ofthe output current, divided by its mean value, has changed from 17.8% to165%. The rms value of the output current divided by the mean value is114%. The rms value of the AC component is 55% of the mean value. Ascould have been expected, these values resemble those of a single phaseLLC resonant voltage converter. This situation, verified in an exemplarytest case, is unacceptable because it would force to size each phaseconverter for delivering the whole output power, without any reductionof the ripple of the output current.

Published U.S. patent application No. 2008/0298093 A1 “Multi-phaseresonant converters for DC-DC application,” discloses a three-phase LLCresonant voltage converter including three half-bridges connected to thesame input bus (re.: the architecture of FIG. 4, in which a furtherphase circuit in parallel to the two depicted phase circuits has beenadded), and shows that it is possible to balance the phase currents.Indeed, only the ideal case of exactly identical converters isconsidered, neglecting spreads among the components.

In U.S. Pat. No. 6,970,366, entitled “Phase-shifted resonant converterhaving reduced output ripple”, a system of two LLC resonant converters,synchronized and mutually phased apart by 90° to minimize the overallripple is disclosed. The document is silent about balancing the twophases.

In the article by H. Figge et al., entitled “Paralleling of LLC resonantconverter using frequency controlled current balancing”, IEEE PESC 2008,June 2008, pp. 1080-1085, a system is disclosed in which a DC-DC buckconversion stage is installed upstream of a two-phases LLC resonantconverter. The regulation loop of the output voltage modulates thevoltage generated by the buck (and, thus, the input voltage of the twohalf-bridges). A regulation loop of the balancing of the currentsthrough the two phases determines the switching frequency of thehalf-bridges that are relatively phased apart by 90°. This architectureaddresses the problem of balancing the currents at the cost of employingan additional conversion stage that reduces overall efficiency andincreases the overall complexity of the converter circuit.

The degree of freedom to balance the currents could be provided byduty-cycle adjustment. In this way, the mean value of the voltageapplied to each phase would be adjustable. Nevertheless, as shown in thesimulations of FIG. 8, this approach may be followed only if smalladjustments are sufficient for obtaining a satisfactory balancing.Indeed, a duty-cycle significantly different from 50% would generatestrongly asymmetrical currents in the secondary windings of thetransformer and in the output diodes, thus the balancing problem wouldbe merely shifted elsewhere. For implementing this method, the reactivecomponents of the resonating circuits would have to be selectedaccurately, which is costly.

The recognized problems of known interleaved resonant architecturescould be resumed, because of their marked sensitivity to differencesamong the power circuits and difficulty of finding a control variablethat would be conveniently used for compensating the consequentunbalancing of the currents among the single phase circuits. This is anindispensable condition for reducing the ripple of the output current,the main reason for implementing the interleaving.

SUMMARY

An architecture of multi-phase resonant converters has been foundcapable of maintaining a good balancing of the currents in each phase,even in the presence of relevant differences among the components of therespective power circuits. This is achieved by connecting the primarywindings and/or the secondary windings of the multi-phase converter toleave the respective real or virtual neutral point floating.

According to an embodiment, the primary windings of the converter may bestar connected, and the real neutral point of the star may be coupled toa node at a reference potential through a normally open auxiliaryswitch. This switch may be closed at low load currents for turning offall the phases of the converter except one.

According to another embodiment, the converter may have a controlcircuit configured to generate pulse width modulation (PWM) drivingsignals mutually phased apart as a function of phase control signalsinput to the control circuit. Current sensors of the current circulatingin each of the primary or secondary windings may be adapted to generaterespective sensing signals, and a circuit may compare the sensingsignals and generate phase control signals that are input to the controlcircuit. With this architecture a control method is implementedaccording to which the PWM driving signals are mutually phased apart forcompensating eventual residual current unbalances.

A control method of the multi-phase resonant converters is alsoprovided. It contemplates the steps of driving only the half-bridge of aphase, leaving on the low-side switch of the half-bridge of anotherphase, and turning off the other half-bridges of the resonant converterwhen the supplied current delivered by the converter becomes smallerthan a pre-established minimum threshold.

The methods may be used with any configuration of the resonant circuit,for example LLC, LCC, or other resonant circuit, independently from thenumber of phases of the converter by connecting the power circuits insuch a way as to leave the real or virtual neutral point of the primaryor of the secondary floating.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a high level schematic block diagram of a typical resonantDC-DC converter according to the prior art.

FIG. 2 is a schematic diagram of an LLC resonant half-bridge with split(center-tap) secondary windings and full wave rectification throughdiodes according to the prior art.

FIG. 3 are graphs of typical waveforms of the converter of FIG. 2 whenoperating near the resonant frequency associated to components Ls andCr.

FIG. 4 is a schematic diagram of an exemplary prior art three-phase LLCresonant converter wherein the interleaving is obtained by relativelyphasing apart by 120° the driving signals of the three half-bridges.

FIG. 5 are graphs of driving signals and currents through each phase ofthe converter of FIG. 4 with hypothetically identical phases.

FIG. 6 is a graph of the transfer characteristic of a half-bridge drivenLLC resonant converter in accordance with the prior art.

FIG. 7 are graphs of waveforms similar to those of FIG. 5, having thecapacitance of the phase circuit 2 is reduced by 10% and the capacitanceof the phase circuit 3 is increased by 10%.

FIGS. 8a-8c are graphs illustrating the effects of a duty-cycleunbalance in a phase circuit.

FIG. 9 is a schematic diagram of an embodiment of a three-phase LLCresonant converter with an isolated neutral point on the primary side inaccordance with the present invention.

FIG. 10 are time graphs of driving signals and of the currents of thephase circuits for the converter of FIG. 9, and under the sameconditions of unbalance of FIG. 7.

FIGS. 11a-11d are graphs of the primary currents and the results of themeasurements of the DC output currents of the phases for the converterof FIG. 9 for the values specified in Table 1.

FIGS. 12a-12d are graphs of the primary currents and the results ofmeasurements of the DC output currents of the phase circuits for theconverter of FIG. 9 with the values specified in Table 1 and with afurther capacitor of 2.7 nF.

FIG. 13 are graphs of waveforms of the main signals of the converter ofFIG. 9 when the phase circuits φ1 and φ2 are active.

FIG. 14 are graphs of waveforms of the main signals of the converter ofFIG. 9 when the sole phase circuit φ1 is active.

FIG. 15 is a schematic diagram of another embodiment of the converter ofFIG. 9 with a normally open auxiliary switch in accordance with thepresent invention.

FIG. 16 are graphs of waveforms of the main signals of the converter ofFIG. 15 when the sole phase circuit φ1 is active and the auxiliaryswitch is closed.

FIGS. 17a-17c are schematic diagrams of regulation loops of the mutualrelative phases of the single phase circuits for nullifying the residualunbalancing of the output currents of each phase circuit in accordancewith the present invention.

FIG. 18 is a graph of the conversion efficiency of the converter of FIG.15 with the parameters defined in Table 1, as a function of the numberof active phase circuits.

FIG. 19 is a graph of the results of simulations of the amplitude of thepeak-to-peak ripple of the output current of the converter with theparameters defined in Table 1 as a function of the number of activephase circuits.

FIG. 20 is a schematic diagram of a second embodiment of a three-phaseLLC resonant converter capable of self-balancing the phase currents inaccordance with the present invention.

FIG. 21 are time graphs of the driving signals and of the phase currentsfor the converter of FIG. 20, with an isolated neutral point at theprimary and under the same unbalance conditions of the waveforms of FIG.7.

FIG. 22 are time graphs of the driving signal and of the phase currentsfor the converter of FIG. 20 with a grounded neutral point at theprimary and under the same unbalance conditions of FIG. 7.

FIG. 23 is a schematic diagram of a third embodiment of a three-phaseLLC resonant converter capable of self-balancing the phase currents inaccordance with the present invention.

FIG. 24 are time graphs of driving signals and of the phase currents ofthe converter of FIG. 23 and in the same unbalance conditions of FIG. 7.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Several exemplary embodiments of this invention will be described makingreference to a three-phase LIC resonant voltage converter, but the sameconsiderations hold also for multi-phase resonant voltage converters ofa different type and/or with any other number of phases.

A three-phase LLC resonant DC-DC voltage converter for limitingunbalance among phase currents is illustrated in FIG. 9. The three LLCresonant circuits on the primary side are connected to a floating commonnode (real neutral point) Fn_(p) different from the prior art converterof FIG. 4 where the neutral point is grounded. The multi-phase resonantDC-DC voltage converter of this disclosure may be controlled using thesame driving signals phased apart by 120° of the half-bridges of theprior art converter of FIG. 4.

The fact that the potential of the neutral-point is not grounded,introduces a “negative feedback” that tends to balance the workingpoints of the single phase circuits, thus preventing a single phasecircuit from delivering the whole current required by the load, whilethe other phase circuits are practically inactive. This is evident inthe graphs of FIG. 10 that illustrate waveforms obtained using the samedriving signals used for the graphs of FIG. 7 relative to the prior artconverter of FIG. 5 under the same unbalance conditions. In themulti-phase resonant voltage converter of this disclosure, the phasecurrents are far more uniform than in the known converter of FIG. 4.

By comparing the time graphs of FIG. 10 with those of FIG. 7, it may berecognized that in the former case, all three phases are working with amaximum unbalance that is 14 times smaller than that of FIG. 7; thepeak-to-peak amplitude of the output current waveform is reduced by afactor larger than 3; and the rms value of the AC current by a factor ofabout 4.

These results are also substantially confirmed by measurements shown inthe graphs of FIGS. 11 and 12, carried out on a prototype formedaccording to the scheme of FIG. 9, and with the design parameters shownin Table 1:

TABLE 1 Minimum DC input voltage Vin_min 320 V Nominal DC input voltageVin 390 V Maximum DC input voltage Vin_max 420 V Regulated outputvoltage Vout  24 V Maximum output current Iout  8 A Nominal resonantcapacitor Cr  22 nF Leakage inductance Lr 110 μH Magnetizationinductance Lm 585 μH Nominal resonant frequency Fr  100 kHz Outputcapacitor Cout 100 μF

In many applications, the performance of the converter of FIG. 9, interms of phase current balance, would be quite acceptable and may notneed any specific further action for improving it. In applications wherean enhanced balance of the phase currents is desired, the converter ofFIG. 9 may be satisfactorily used, though the mutual relative phasesbetween driving signals of the half-bridges may be adjusted. Relativephasing introduces a degree of freedom, that is a control variable forimplementing a regulation loop to nullify any residual unbalance amongthe phase currents.

Well known techniques for carrying out such a feedback control may beimplemented by any skilled person. For example, it may be possible tosense the secondary currents or the resonant primary currents; thesensing may be performed through a current transformer or throughsensing resistors; and the error signals may be generated and processedthrough mutual comparisons and/or with reference values, or by the useof error amplifiers with frequency compensations, or even through analogor digital processing. Control may be implemented by leaving a phasecircuit fixed, driving it with unmodified drive signals, and modulatingthe driving signals of the other phase circuits, or by modulating allthe driving signals of the phase circuits, etc. The skilled designerwill choose the most appropriate control technique in consideration ofdesign specifications, characteristics, performance of the converter,and cost restraints.

When the output load is relatively low, the multi-phase resonantconverter may be controlled also by driving only two phase circuits andleaving the other phase circuit(s) isolated, as illustrated in thegraphs of FIG. 13, to improve the conversion efficiency. As it may benoticed, even in this functioning condition, the two active phases arebalanced.

It may also be possible to drive a single half-bridge of the multi-phaseresonant converter when the converter delivers relatively low currents.This may be done by keeping on one or more low-side switches of anotherhalf-bridge to close the circuit. Exemplary graphs obtained by drivingthe converter of FIG. 9 in such a functioning condition are shown inFIG. 14.

FIG. 15 illustrates another embodiment of the multiphase converterhaving a normally off auxiliary switch S_(aux) for grounding the realneutral point np_(p) of the primary circuit. If the converter has todeliver a relatively low output current, only a half-bridge is driven,and the other half-bridges are kept off and the auxiliary switch isclosed. An exemplary time diagram obtained in this functioning conditionis illustrated in the graphs of FIG. 16.

Experimental results, illustrated in the graph 1800 of FIG. 18, showthat the efficiency improves at medium-low load conditions. Therefore,it may be desirable to turn off a phase circuit when the load decreasesbelow 55% of the maximum rated load (see curve 1804), and operate with asingle phase circuit when the load becomes smaller than 30% of themaximum load (see curve 1806).

When only two phase circuits are active, it may be desirable to drivethe two half-bridges in phase opposition: when the third phase circuitis switched off, the phase regulation loop, if present, is disabled andthe relative phase varies from 120° (or a value not much different fromthis value, in case the phase regulation loop is present) to 180°. Inthis case the converter is driven in a full-bridge mode.

The characteristics of the resonant circuit are only slightly modified:both the inductances and the resonant capacitances are coupled inseries. If the two resonant circuits were identical, the resonantfrequency would not change; the characteristic impedance doubles but,since the two secondary circuits are electrically coupled in parallel,the quality factor Q remains unchanged. Small differences are presentbecause the two resonant circuits do not match exactly, and thus theregulation loop of the output voltage of the converter may act in alimited manner for correcting the working frequency.

One or more low-side MOSFETs of the inactive half-bridges may be kept onfor allowing current to circulate through a single phase circuit. In thefirst case, the resonant circuit, switching from two active phasecircuits to one active phase circuit, is not (nominally) altered;nevertheless, the functioning conditions switch abruptly from afull-bridge to a half-bridge mode, consequently halving the gain. Thisplaces a heavy burden on the regulation loop of the output voltage ofthe converter to compensate for the abrupt gain variation with anappropriate reduction of the working frequency. In the latter case, allphase circuits participate in the delivery of energy (even if in anunbalanced manner), but with a great variation of the characteristics ofthe resonant circuit. Thus, also in this case, the regulation loop ofthe output voltage should be able to reduce the working frequency.

Other exemplary architectures of multiphase resonant converters areillustrated in FIGS. 17a-17c . These converters have sensors (e.g.,sensors 1702, 1704, 1706, 1708, 1710, 1712, 1714, 1716) of the currentcirculating in the primary or secondary windings and configured togenerate respective sensing signals (e.g., signals S₁₇₀₂, S₁₇₀₄, S₁₇₀₆,S₁₇₀₈, S₁₇₁₀, S₁₇₁₂, S₁₇₁₄, S₁₇₁₆) and a comparison circuit (e.g., 1720)that generates phase control signals by comparing the sensing signalsamong each other. These phase control signals are used for adjustingmutual relative phase among the driving signals of the half-bridges tofurther balance the functioning conditions of the distinct phasecircuits of the converter.

According to an embodiment, the comparison circuit senses the differencebetween the currents of the phase circuit 1 (φ1) and of the phasecircuit 2 (φ2), and between the currents of the phase circuit 2 (φ2) andof the phase circuit 3 (φ3), generating phase control signals (Δφ₁₋₂,Δφ₂₋₃). Using these phase control signals, mutual relative phasesbetween the driving signal of MOSFErs of phase circuit 2 in respect tothat of phase circuit 1 (that, for example, may be considered as areference), and the relative phases between the driving signals of theMOSFETs of phase circuit 3 in respect to that of phase circuit 2 areadjusted. Table 2 shows exemplary comparison data for evaluating theeffect of a correction carried out by the relative phase regulation loopand the consequent reduction of unbalance among the output currents ofthe distinct phase circuit.

TABLE 2 No With relative relative Load phase phase current controlcontrol 5A DC output current 1.64 A 1.64 A of phase circuit 1 (−1.2%)(−2.6%) DC output current 1.60 A 1.73 A of phase circuit 2 (−10.2%)(+2.6%) DC output current 1.85 A 1.67 A of phase circuit 3 (+11.2%) (0%)6A DC output current 1.98 A 1.94 A of phase circuit 1 (−1.65%) (−3.6%)DC output current 1.84 A 2.08 A of phase circuit 2 (−8.6%) (3.1%) DCoutput current 2.23 A 2.02 A of phase circuit 3 (10.4%) (0.33%)

The values of parameters of the relative phase regulation loop forcorrecting the residual unbalance among the phase currents may be evendifferent from the above indicated values. The values of the parametersmay be designed according to the characteristics of the application inwhich the converter is to be used.

The results of a simulation carried out on one of the convertersschematically illustrated in FIGS. 17a-17c with the parameters indicatedin Table 1 are graphically illustrated in FIG. 19. To make the outputcurrent ripple not exceed the value attained at maximum load when allthe three phase circuits are active, the converter may work with onlytwo active phase circuits (e.g., curve 1904) for loads smaller than 15%of the maximum load, and with a single active phase circuit (e.g., curve1902) for loads smaller than 10% of the maximum load. The optimalcompromise between the two will be determined by design consideringspecifications, characteristics, performance of the converter, and costrestraints.

Another example of a three-phase LLC resonant voltage converter havingan intrinsic ability of limiting unbalance among phase currents isschematically illustrated in FIG. 20. Even in this case, the three LLCresonant circuits at the primary are connected to the isolated realneutral point np_(p); the transformers have a single secondary (havinghalf the number of turns of the secondary windings of the transformersused in the architecture of FIG. 9); and the three circuits are coupledto a floating neutral-point Fns of the secondary circuit. The rectifiers2002 form a three-phase bridge.

FIG. 21 graphically shows the waveforms of the driving signals of thehalf-bridges (also in this case phased apart by 120°) and the waveformsof the primary and secondary currents of the converter of FIG. 20. Inthis case, the reference capacitors Cr are not identical for all thephase circuits, but the capacitor of the phase circuit 2 is reduced by10% and the capacitor of the phase circuit 3 is increased by 10%. Inthese conditions, similar to those used for treating the architecture ofthe preceding embodiment, the residual unbalance and the peak-to-peakripple are slightly smaller.

The architecture of the converter of this disclosure simplifies thetransformer. It may not be necessary to form two accurately symmetricalsecondary windings, as in known converters with split (center-tap)secondary winding. The number of turns is halved, but the rms currentthat flows therethrough is doubled thus, neglecting high frequencyeffects, with the same amount of copper used for the windings.Conduction losses remain the same. However, because of the reducednumber of turns, the magnitude of high frequency effects is reduced.

Because the neutral point of the secondary circuit is floating, it maybe no longer desirable to leave the neutral point of the primary circuitnp floating (grounding it as shown in FIG. 20). However, the converterarchitecture remains effective in reducing unbalance among the phasecurrents.

The results of simulations graphed in FIG. 22 show only marginaldifferences with respect to those of FIG. 21, with only a slightdeformation of primary currents, while the secondary currents remainsubstantially unchanged, and performance is substantially the same. Withthis architecture, whether the primary neutral point is floating or not,it may be possible to further reduce the unbalance among the phasecurrents through a relative phase control loop. This relative phasecontrol may be employed also for the topology of FIG. 9.

FIG. 23 illustrates a further embodiment of a three-phase LIC resonantcircuit intrinsically capable of limiting the unbalance among the phasecurrents. Compared to the architecture of FIG. 20, the connections ofthe secondary circuits are the same, and the primary circuits aretriangle connected. Even in this case, the neutral point (that in thisconfiguration is virtual and not real) is floating. Given that theprimary voltage is larger, the number of turns of the secondary windingsis smaller than that of the architecture of FIG. 20.

The graph of FIG. 24 illustrates the waveforms of the driving signals ofthe half-bridges (also in this case phased apart by 120°) and thewaveforms of the primary and secondary currents when the capacitance ofthe phase circuit 2 is reduced by 10% and the capacitance of the phasecircuit 3 is increased by 10%. Compared to the conditions used fortesting the previous architectures, the residual unbalance and theincrease of the output current ripple are slightly smaller than theother architectures. Also for this architecture, it may be possible tofurther reduce the unbalance among the phase currents by employing arelative phase control loop, as compared to the other two previouslydescribed architectures.

1. A multi-phase resonant LLC converter comprising: a plurality of phasecircuits; a plurality of primary windings coupled to the plurality ofphase circuits; a plurality of capacitors electrically coupled to theplurality of primary windings; and a plurality of secondary windingsmagnetically coupled to the plurality of primary windings, wherein themulti-phase resonant LLC converter is configured to balance currentsflowing through the plurality of primary windings using a floating node,and wherein each of the plurality of primary windings is coupled to thefloating node via respective passive components of a plurality ofpassive components.
 2. The multi-phase resonant LLC converter of claim1, wherein the plurality of passive components is the plurality ofcapacitors so that each of the plurality of primary windings is coupledto the floating node via a respective capacitor of the plurality ofcapacitors.
 3. The multi-phase resonant LLC converter of claim 1,wherein: the plurality of phase circuits comprises first, second, andthird phase circuits; the plurality of primary windings comprises first,second, and third primary windings coupled to the first, second, andthird phase circuits, respectively; the plurality of secondary windingscomprises first, second, and third secondary windings magneticallycoupled to the first, second, and third primary windings, respectively;and the plurality of capacitors comprises first, second, and thirdcapacitors coupled to the first, second, and third primary windings,respectively.
 4. The multi-phase resonant LLC converter of claim 1,wherein each of the plurality of phase circuits comprises a respectivehalf-bridge.
 5. The multi-phase resonant LLC converter of claim 4,wherein each half-bridge of the plurality of phase circuits comprises ahigh-side n-type transistor and a low-side n-type transistor.
 6. Themulti-phase resonant LLC converter of claim 5, the high-side andlow-side n-type transistors of each respective half-bridge is atransistor of the metal-oxide semiconductor field-effect transistor(MOSFET) type.
 7. The multi-phase resonant LLC converter of claim 1,further comprising: an output terminal; and a plurality of rectifyingcircuits respectively coupled between each of the plurality of secondarywindings and the output terminal.
 8. The multi-phase resonant LLCconverter of claim 7, further comprising an output capacitor coupled tothe output terminal, wherein each of the plurality of rectifyingcircuits comprises first and second diodes having cathodes coupled tothe output capacitor.
 9. The multi-phase resonant LLC converter of claim1, wherein each of the plurality of secondary windings is a center-tapwinding.
 10. The multi-phase resonant LLC converter of claim 9, whereineach center-tap of the plurality of secondary windings is coupled to areference node.
 11. The multi-phase resonant LLC converter of claim 1,wherein each secondary winding of the plurality of secondary windings iscoupled to a second floating node.
 12. The multi-phase resonant LLCconverter of claim 11, wherein each secondary winding is directlyconnected to the second floating node.
 13. The multi-phase resonant LLCconverter of claim 11, further comprising a plurality of current sensorsconfigured to sense winding currents flowing through each of theplurality of primary windings.
 14. A multi-phase resonant LLC convertercomprising: a plurality of phase circuits; a plurality of primarywindings coupled to the plurality of phase circuits; a plurality ofcapacitors electrically coupled to the plurality of primary windings;and a plurality of secondary windings magnetically coupled to theplurality of primary windings, wherein the multi-phase resonant LLCconverter is configured to balance currents flowing through theplurality of primary windings using a floating node, and wherein eachsecondary winding of the plurality of secondary windings is coupled tothe floating node.
 15. The multi-phase resonant LLC converter of claim14, wherein: the plurality of phase circuits comprises first, second,and third phase circuits; the plurality of primary windings comprisesfirst, second, and third primary windings coupled to the first, second,and third phase circuits, respectively; the plurality of secondarywindings comprises first, second, and third secondary windingsmagnetically coupled to the first, second, and third primary windings,respectively; and the plurality of capacitors comprises first, second,and third capacitors coupled to the first, second, and third primarywindings, respectively.
 16. The multi-phase resonant LLC converter ofclaim 14, wherein each of the plurality of phase circuits comprises arespective half-bridge.
 17. The multi-phase resonant LLC converter ofclaim 16, wherein each half-bridge of the plurality of phase circuitscomprises a high-side n-type transistor and a low-side n-typetransistor.
 18. The multi-phase resonant LLC converter of claim 17, thehigh-side and low-side n-type transistors of each respective half-bridgeis a transistor of the metal-oxide semiconductor field-effect transistor(MOSFET) type.
 19. The multi-phase resonant LLC converter of claim 14,further comprising a first diode having an anode coupled to a firstsecondary winding of the plurality of secondary windings.
 20. Themulti-phase resonant LLC converter of claim 14, wherein each secondarywinding of the plurality of secondary windings is directly connected tothe floating node.
 21. The multi-phase resonant LLC converter of claim14, further comprising a plurality of rectification circuits coupled tothe plurality of secondary windings, each rectification circuit of theplurality of rectification circuits coupled to a respective firstterminal of respective secondary windings of the plurality of secondarywindings, wherein a second terminal of each secondary winding of theplurality of secondary windings is coupled to the floating node.
 22. Athree-phase resonant LLC converter comprising: first, second, and thirdphase circuits; first, second, and third primary windings coupled to thefirst, second, and third phase circuits, respectively, first, second,and third secondary windings magnetically coupled to the first, second,and third primary windings, respectively; and first, second, and thirdcapacitors coupled to the first, second, and third primary windings,respectively, wherein the first, second, and third secondary windingsare directly connected to a neutral point that is electrically floating.23. The three-phase resonant LLC converter of claim 22, furthercomprising a first diode having an anode directly connected to the firstsecondary winding.